Problem: In how many ways can 6 distinct beads be placed on a bracelet? (Note that two arrangements are the same if one can be rotated or reflected to produce the other.)
There are $6!$ ways to place the beads on the bracelet, but we must divide by 6 for rotational symmetry (6 rotations for each arrangement), and by 2 for reflectional symmetry (we can flip the bracelet to get the same arrangement).  The answer is $\dfrac{6!}{6 \times 2} = \boxed{60}$.